Kirchhoff Yaklaşımı İntegralinin Radon Dönüşümü Yorumu ile Zaman Uzayında Belirlenmesi Üzerine

Öz

Bu çalışmada, düzlemsel dalga ile aydınlatılmış, yumuşak ve sert saçıcılardan oluşan uzak alandaki akustik saçılmanın, Kirchhoff yaklaşımı (KY) ile zaman uzayında analizinde ortaya çıkan ışıma integralinin kapalı-formda belirlenmesi gösterilmiştir. Özel olarak KY ile ortaya çıkan ışıma integralinin, elektromanyetikteki eşdeğeri olan fiziksel optik (FO) yaklaşımı kullanıldığında oluşan ışıma integrali aynı olduğu gösterilmiştir. Sonuç olarak FO yaklaşımı için Radon dönüşümü yorumu ile geliştirilen kapalı-form ifade doğrudan KY için kullanılabilir. Kapalı-form ifadelerinin doğruluğu bir nümerik örnekle gösterilmiştir.

Anahtar Kelimeler

• Akustik saçılma
• Kirchhoff yaklaşımı
• zaman uzayı analizi

On the Evaluation of the Kirchhoff Approximation Integral using Radon Transform Interpretation in Time Domain

Öz

In this work, closed-form evaluation of the radiation integral to determine the time domain acoustic scattered fields at the far zone for soft and hard scatterers using Kirchhoff approximation (KA) under plane-wave illumination is presented. Specifically, it is shown that the radiation integral for KA is the same as the physical optics (PO) integral, which is the equivalent of KA in electromagnetics, for perfect electrically conducting scatterers. Consequently, the closed-form expression of the PO integral developed using Radon transform interpretation can be used in KA directly. The validity of the closed-form expression is demonstrated via a numerical example.

Anahtar Kelimeler

• Acoustic scattering
• Kirchhoff approximation
• time domain analysis

Kaynakça

1. [1] J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, John Wiley and Sons, 1969.
2. [2] T. B. Hansen and A. D. Yaghjian, Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications, Wiley-IEEE Press, 1999.
3. [3] D. S. Jones, Acoustic and Electromagnetic Waves, Oxford: Clarendon Press, 1986.
4. [4] W. B. Gordon, “Far-field approximations to the Kirchoff-Helmholtz representations of scattered fields,” IEEE T Antenn Propag, vol. 23, no. 4, pp. 590-592, July 1975.
5. [5] W. B. Gordon, “High frequency approximations to the physical optics scattering integral,” IEEE T Antenn Propag, vol. 42, no. 3, pp. 427-432, Mar. 1994.
6. [6] D. Bölükbaş and A. A. Ergin, “A Radon transform interpretation of the physical optics integral,” Microw Opt Technol Lett, vol. 44, no. 3, pp. 284–288, 2005.
7. [7] H. A. Serim and A. A. Ergin, “Computation of the physical optics integral on NURBS surfaces using a Radon transform interpretation,” IEEE Antenn Wirel Propag Lett, vol. 7, pp. 70-73, 2008.
8. [8] S. Karaca and A. A. Ergin, “Closed-form time domain PO expressions of the electric field scattered from PEC objects illuminated by an electric dipole,” IEEE T Antenn Propag, vol. 63, no. 10, pp. 4477-4485, Oct. 2015.

9. [9] A. Aktepe and H. A. Ülkü, “On the closed-form evaluation of the PO integral using the Radon transform interpretation for linear triangles,” Turk J Electr Eng Comput Sci, vol. 29, no. 5, Article 17, 2021.
10. [10]A. Aktepe and H. A. Ülkü, “Exact evaluation of time-domain physical optics integral on quadratic triangular surfaces,” IEEE T Antenn Propag, vol. 68, no. 11, pp. 7447-7456, Nov. 2020.
11. [11]A. Aktepe and H. A. Ülkü, “Exact evaluation of time domain physical optics integral for high order triangles,” IEEE T Antenn Propag, vol. 71 (Early Access).
12. [12]F. Vico-Bondia, M. Ferrando-Bataller, and A. Valero-Nogueira, “A new fast physical optics for smooth surfaces by means of a numerical theory of diffraction,” IEEE T Antenn Propag, 58 (3), 773–789, 2010.
13. [13]Y. M. Wu, L. J. Jiang, W. E. I. Sha, and W. C. Chew, “The numerical steepest descent path method for calculating physical optics integrals on smooth conducting quadratic surfaces,” IEEE T Antenn Propag, vol. 61, no. 8, pp. 4183- 4193, Aug. 2013.
14. [14]H. Kobayashi, K. Hongo, and I. Tanaka, “Expressions of physical optics integral for smooth conducting scatterers approximated by quadratic surfaces,” Electron and Commun in Japan (Part I: Commun), vol. 83, no. 7, pp. 61– 70, 2000.
15. [15]M. Domingo, F. Rivas, J. Perez, R. P. Torres, and M. F. Catedra, “Computation of the RCS of complex bodies modeled using NURBS surfaces,” IEEE Antenn Propag M, vol. 37, no. 6, pp. 36-47, Dec. 1995.
16. [16]A. C. Yucel and A. A. Ergin, “Exact evaluation of retarded-time potential integrals for the RWG bases,” in IEEE T Antenn Propag, vol. 54, no. 5, pp. 1496-1502, May 2006.
17. [17]H. A. Ülkü and A. A. Ergin, “Analytical evaluation of transient magnetic fields due to RWG current bases,” IEEE T Antenn Propag, vol. 55, no. 12, pp. 3565-3575, Dec. 2007.
18. [18]H. A. Ülkü and A. A. Ergin, “Application of analytical retarded-time potential expressions to the solution of time domain integral equations,” IEEE T Antenn Propag, vol. 59, no. 11, pp. 4123-4131, Nov. 2011.
19. [19]H. A. Ülkü, A. A. Ergin, and F. Dikmen, “On the evaluation of retarded-time potentials for SWG bases,” IEEE Antenn Wirel Propag Lett, vol. 10, pp. 187-190, 2011.
20. [20]F. Dikmen, “On analytical evaluation of retarded-time potentials for SWG bases,” IEEE T Antenn Propag, vol. 62, no. 9, pp. 4860-4863, Sept. 2014.